Since this is actually an algae and not a true seaweed, it will break down quite quickly when piled up like a compost heap, algae tends to be somewhat problematic since when it dries it crumbles to dust.
I agree that there is a great opportunity for a business to spring up in removal and then selling the composted algae as a soil amendment, no washing needed, just build large heaps and let it go.
The business would need either land or perhaps sea going barges, barges could be used both for collecting and for composting, from that point you would need bagging equipment and marketing of the product.
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